The objective of this research is to gain a better understanding of the dynamic role played by stress and strain on the remodeling and growth of the blood vessels. When blood pressure or flow is increased above the normal, changes occur in the blood vessel lumen, wall thickness, zero- stress state, fine structure of the intima, media and adventitia layers, geometry and dimensions of the endothelial and smooth muscle cells, the mechanical properties of the intima-media and adventitial layers, capillaries, and even branching patterns and total generation numbers. Hence our HYPOTHESIS: Stress and strain are important factors that determine blood vessel structure and function, together with chemical factors. We want to document their influence mathematically, with the following SPECIFIC AIMS: 1) To determine the effects of changing blood shear and blood pressure on the remodeling of the blood vessels and express them in the form of indicial functions. 2) To obtain data on the morphology, histology and experimental mechanics of vessels and use them to calculate the stress and strain distribution and determine the strain energy functions of the intima-media and adventitia layers which change in the remodeling process. 3) To demonstrate the applications of the results by solving some key problems of the heart. The biology of growth and remodeling should be studied at all levels from atoms to the whole animal. The scale of the level chosen for the present study is that of the tissue with a minimum dimension in the mu-m range. In this length scale, our RATIONALE is that the engineering approach is the most efficient, in which questions in physiology and medicine can be converted to boundary - value problems whose solutions can be tested experimentally. In the process, we correct a current deficiency in biomedical science: people really do not know how to compute stress and strain in the tissues of blood vessels. We will make an effort to give biomechanics a firm foundation.